Stochastic Fluctuations Research Articles

Dynamical Analysis of an Improved Bidirectional Immunization SIR Model in Complex Network.

In order to investigate the impact of two immunization strategies-vaccination targeting susceptible individuals to reduce their infection rate and clinical medical interventions targeting infected individuals to enhance their recovery rate-on the spread of infectious diseases in complex networks, this study proposes a bilinear SIR infectious disease model that considers bidirectional immunization. By analyzing the conditions for the existence of endemic equilibrium points, we derive the basic reproduction numbers and outbreak thresholds for both homogeneous and heterogeneous networks. The epidemic model is then reconstructed and extensively analyzed using continuous-time Markov chain (CTMC) methods. This analysis includes the investigation of transition probabilities, transition rate matrices, steady-state distributions, and the transition probability matrix based on the embedded chain. In numerical simulations, a notable concordance exists between the outcomes of CTMC and mean-field (MF) simulations, thereby substantiating the efficacy of the CTMC model. Moreover, the CTMC-based model adeptly captures the inherent stochastic fluctuation in the disease transmission, which is consistent with the mathematical properties of Markov chains. We further analyze the relationship between the system's steady-state infection density and the immunization rate through MCS. The results suggest that the infection density decreases with an increase in the immunization rate among susceptible individuals. The current research results will enhance our understanding of infectious disease transmission patterns in real-world scenarios, providing valuable theoretical insights for the development of epidemic prevention and control strategies.

Somatodendritic organization of pacemaker activity in midbrain dopamine neurons.

The slow and regular pacemaking activity of midbrain dopamine (DA) neurons requires proper spatial organization of the excitable elements between the soma and dendritic compartments, but the somatodendritic organization is not clear. Here, we show that the dynamic interaction between the soma and multiple proximal dendritic compartments (PDCs) generates the slow pacemaking activity in DA neurons. In multipolar DA neurons, spontaneous action potentials (sAPs) consistently originate from the axon-bearing dendrite. However, when the axon initial segment was disabled, sAPs emerge randomly from various primary PDCs, indicating that multiple PDCs drive pacemaking. Ca2+ measurements and local stimulation/perturbation experiments suggest that the soma serves as a stably-oscillating inertial compartment, while multiple PDCs exhibit stochastic fluctuations and high excitability. Despite the stochastic and excitable nature of PDCs, their activities are balanced by the large centrally-connected inertial soma, resulting in the slow synchronized pacemaking rhythm. Furthermore, our electrophysiological experiments indicate that the soma and PDCs, with distinct characteristics, play different roles in glutamate- induced burst-pause firing patterns. Excitable PDCs mediate excitatory burst responses to glutamate, while the large inertial soma determines inhibitory pause responses to glutamate. Therefore, we could conclude that this somatodendritic organization serves as a common foundation for both pacemaker activity and evoked firing patterns in midbrain DA neurons.

Measurements of Turbulence in Compressible Low-Density Flows at the Inlet of a Transonic Linear Cascade With and Without Unsteady Wakes

Abstract In the present work, hot-wire anemometry was employed for the characterization of the turbulent field at the inlet of a high-speed low-pressure turbine cascade, in terms of turbulence intensity and integral length scales. This work addresses two major topics relevant to the turbomachinery field: the application of hot-wire anemometry in transonic and rarefied flow regimes and the decoupling of the deterministic and the stochastic fluctuations when measuring unsteady phenomena. In compressible and rarefied flows, a hot-wire is strongly sensitive to both density and velocity fluctuations, and the commonly used Nusselt–Reynolds correlations are not valid. In this article, a nondimensional calibration methodology, based on Nusselt, Reynolds, and Knudsen numbers, was coupled with a sensitivity analysis and employed to postprocess the experimental dataset, allowing to decouple the fluctuations of density and velocity and to compute the turbulence parameters. In the presence of unsteady wakes generated upstream of the cascade, two different phase-locked averaging techniques were employed to distinguish the wake deterministic fluctuations from the background turbulence intensity.

Energy-based stochastic resetting can avoid noise-enhanced stability.

The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced stability. This phenomenon implies that under specific noise amplitudes the escape process is delayed. Here, we propose a protocol for stochastic resetting that can avoid the noise-enhanced stability effect. In our approach, instead of resetting the trajectories at certain time intervals, a trajectory is reset when a predefined energy threshold is reached. The trajectories that delay the escape process are the ones that lower their energy due to the stochastic fluctuations. Our resetting approach leverages this fact and avoids long transients by resetting trajectories before they reach low-energy levels. Finally, we show that the chaotic dynamics (i.e., the sensitive dependence on initial conditions) catalyzes the effectiveness of the resetting strategy.

Reinforcement learning based two‐timescale energy management for energy hub

AbstractMaintaining energy balance and economical operation is significant for energy hub (EH) which serves as the central component. Implementing real‐time regulation for heating and cooling equipment within the EH is challenging due to their slow response time in response to the stochastic fluctuation in renewable energy sources and demands while the opposite is true for electric energy storage equipment (EST), a conventional single timescale energy management strategy is no longer sufficient to take into account the operating characteristics of all equipment. With this motivation, this study proposes a deep reinforcement learning based two‐timescale energy management strategy for EH, which controls heating & cooling equipment on a long timescale of 1 h, and EST on a short timescale of 15 min. The actions of the EST are modelled as discrete to reduce the action spaces, and the discrete‐continuous hybrid action sequential TD3 model is proposed to address the problem of handling both discrete and continuous actions in long timescale policy. A joint training approach based on the centralized training framework is proposed to learn multiple levels of policies in parallel. The case studies demonstrate that the proposed strategy reduces the economic cost and carbon emissions by 1%, and 0.5% compared to the single time‐scale strategy respectively.

Blinking characteristics of organic fluorophores for blink-based multiplexing

Single-molecule fluorescence experiments have transformed our understanding of complex materials and biological systems. Whether single molecules are used to report on their nano-environment or provide for localization, understanding their blinking dynamics (i.e., stochastic fluctuations in emission intensity under continuous illumination) is paramount. We recently demonstrated another use for blinking dynamics called blink-based multiplexing (BBM), where individual emitters are classified using a single excitation laser based on blinking dynamics, rather than color. This study elucidates the structure-activity relationships governing BBM performance in a series of model rhodamine, BODIPY, and anthraquinone fluorophores that undergo different photo-physical and-chemical processes during blinking. Change point detection and multinomial logistic regression analyses show that BBM can leverage spectral fluctuations, electron and proton transfer kinetics, as well as photostability for molecular classification—even within the context of a shared blinking mechanism. In doing so, we demonstrate two- and three-color BBM with ≥ 93% accuracy using spectrally-overlapped fluorophores.

Spatial constraints and stochastic seeding subvert microbial arms race.

Surface attached communities of microbes grow in a wide variety of environments. Often, the size of these microbial community is constrained by their physical surroundings. However, little is known about how size constraints of a colony impact the outcome of microbial competitions. Here, we use individual-based models to simulate contact killing between two bacterial strains with different killing rates in a wide range of community sizes. We found that community size has a substantial impact on outcomes; in fact, in some competitions the identity of the most fit strain differs in large and small environments. Specifically, when at a numerical disadvantage, the strain with the slow killing rate is more successful in smaller environments than in large environments. The improved performance in small spaces comes from finite size effects; stochastic fluctuations in the initial relative abundance of each strain in small environments lead to dramatically different outcomes. However, when the slow killing strain has a numerical advantage, it performs better in large spaces than in small spaces, where stochastic fluctuations now aid the fast killing strain in small communities. Finally, we experimentally validate these results by confining contact killing strains of Vibrio cholerae in transmission electron microscopy grids. The outcomes of these experiments are consistent with our simulations. When rare, the slow killing strain does better in small environments; when common, the slow killing strain does better in large environments. Together, this work demonstrates that finite size effects can substantially modify antagonistic competitions, suggesting that colony size may, at least in part, subvert the microbial arms race.

An Examination of Polarization Mode Transitions in Pulsar Radio Emission

A statistical model is used to determine how stochastic fluctuations in the intensities of orthogonal polarization modes contribute to the modulation and depolarization of pulsar radio emission. General expressions for the distributions of the Stokes parameters, linear polarization, polarization position angle, and fractional polarization are derived when the mode intensities follow the same or different probability distributions. The transition between modes is examined. When the mode intensities follow the same distribution, the fractional linear polarization and modulation index are symmetric about the transition. The symmetry is disrupted when the mode intensities follow different distributions. The fractional linear polarization is minimum and the mode frequency of occurrence changes rapidly at transitions where the mode intensity distributions are the same and the modulation index is small. A lower limit on the fractional linear polarization that can be attained via the simultaneous occurrence of the modes as a function of modulation index is quantified.

Helical motors and formins synergize to compact chiral filopodial bundles: A theoretical perspective

Chiral actin bundles have been shown to play an important role in cell dynamics, but our understanding of the molecular mechanisms which combine to generate chirality remains incomplete. To address this, we numerically simulate a crosslinked filopodial bundle under the actions of helical myosin motors and/or formins and examine the collective buckling and twisting of the actin bundle. We first show that a number of proposed mechanisms to buckle polymerizing actin bundles without motor activity fail under biologically-realistic parameters. We then demonstrate that a simplified model of myosin spinning action at the bundle base effectively “braids” the bundle, but cannot control compaction at the fiber tips. Finally, we show that formin-mediated polymerization and motor activity can act synergitically to compact filopodium bundles, as motor activity bends filaments into shapes that activate twist forces induced by formins. Stochastic fluctuations of actin polymerization rates and slower cross linking dynamics both increase buckling and decrease compaction. We discuss implications of our findings for mechanisms of cytoskeletal chirality.

Retracted: Prediction of High-Frequency Economic Data Based on Stochastic Fluctuation Model

Retracted: Prediction of High-Frequency Economic Data Based on Stochastic Fluctuation Model

Stochastic fluctuations of diluted pedestrian dynamics along curved paths.

As we walk towards our destinations, our trajectories are constantly influenced by the presence of obstacles and infrastructural elements; even in the absence of crowding our paths are often curved. Since the early 2000s pedestrian dynamics have been extensively studied, aiming at quantitative models with both fundamental and technological relevance. Walking kinematics along straight paths have been experimentally investigated and quantitatively modeled in the diluted limit (i.e., in absence of pedestrian-pedestrian interactions). It is natural to expect that models for straight paths may be an accurate approximations of the dynamics even for paths with curvature radii much larger than the size of a single person. Conversely, as paths curvature increase one may expect larger and larger deviations. As no clear experimental consensus has been reached yet in the literature, here we accurately and systematically investigate the effect of paths curvature on diluted pedestrian dynamics. Thanks to a extensive and highly accurate set of real-life measurements campaign, we derive a Langevin-like social-force model quantitatively compatible with both averages and fluctuations of the walking dynamics. Leveraging on the differential geometric notion of covariant derivative, we generalize previous work by some of the authors, effectively casting a Langevin social-force model for the straight walking dynamics in a curved geometric setting. We deem this the necessary first step to understand and model the more general and ubiquitous case of pedestrians following curved paths in the presence of crowd traffic.

Dissipative Dynamics of Graph-State Stabilizers with Superconducting Qubits.

We study experimentally and numerically the noisy evolution of multipartite entangled states, focusing on superconducting qubit devices accessible via the cloud. We find that a valid modeling of the dynamics requires one to properly account for coherent frequency shifts, caused by stochastic charge-parity fluctuations. We introduce an approach modeling the charge-parity splitting using an extended Markovian environment. This approach is numerically scalable to tens of qubits, allowing us to simulate efficiently the dissipative dynamics of some large multiqubit states. Probing the continuous-time dynamics of increasingly larger and more complex initial states with up to 12 coupled qubits in a ring-graph state, we obtain a good agreement of the experiments and simulations. We show that the underlying many-body dynamics generate decays and revivals of stabilizers, which are used extensively in the context of quantum error correction. Furthermore, we demonstrate the mitigation of 2-qubit coherent interactions (crosstalk) using tailored dynamical decoupling sequences. Our noise model and the numerical approach can be valuable to advance the understanding of error correction and mitigation and invite further investigations of their dynamics.

Intermittent power smoothing control for grid connected hybrid wind/PV system using battery-EDLC storage devices

Wind and solar radiation are intermittent with stochastic fluctuations, which can influence the stability of operation of the hybrid system in the grid integrated mode of operation. In this research work, a smoothing control method for mitigating output power variations for a grid integrated wind/PV hybrid system using a battery and electric double layer capacitor (EDLC) is investigated. The power fluctuations of the hybrid system are absorbed by a battery and EDLC during wide variations in power generated from the solar and wind system, subsequently, the power supplied to the grid is smoothened. This makes higher penetration and incorporation of renewable energy resources to the utility system possible. The control strategy of the inverter is realized to inject the power to the utility system with the unity power factor and a constant DC bus voltage. Both photovoltaic (PV) and wind systems are controlled for extracting maximum output power. In order to observe the performance of the hybrid system under practical situations in smoothing the output power fluctuations, one-day practical site wind velocity and irradiation data are considered. The dynamic modeling and effectiveness of this control method are verified in the MATLAB/Simulink environment. The simulation results show that the output power variations of the hybrid wind/PV system can be significantly mitigated using the combination of battery and EDLC based storage systems. The power smoothing controller proposed for the hybrid storage devices is advantageous as compared to the control technique which uses either battery or ultracapacitor used for smoothing the fluctuating power

Two Determinants of Dynamic Adaptive Learning for Magnitudes and Probabilities.

Humans face a dynamic world that requires them to constantly update their knowledge. Each observation should influence their knowledge to a varying degree depending on whether it arises from a stochastic fluctuation or an environmental change. Thus, humans should dynamically adapt their learning rate based on each observation. Although crucial for characterizing the learning process, these dynamic adjustments have only been investigated empirically in magnitude learning. Another important type of learning is probability learning. The latter differs from the former in that individual observations are much less informative and a single one is insufficient to distinguish environmental changes from stochasticity. Do humans dynamically adapt their learning rate for probabilities? What determinants drive their dynamic adjustments in magnitude and probability learning? To answer these questions, we measured the subjects' learning rate dynamics directly through real-time continuous reports during magnitude and probability learning. We found that subjects dynamically adapt their learning rate in both types of learning. After a change point, they increase their learning rate suddenly for magnitudes and prolongedly for probabilities. Their dynamics are driven differentially by two determinants: change-point probability, the main determinant for magnitudes, and prior uncertainty, the main determinant for probabilities. These results are fully in line with normative theory, both qualitatively and quantitatively. Overall, our findings demonstrate a remarkable human ability for dynamic adaptive learning under uncertainty, and guide studies of the neural mechanisms of learning, highlighting different determinants for magnitudes and probabilities.

A Hybrid Model for Long-Term Wind Power Forecasting Utilizing NWP Subsequence Correction and Multi-Scale Deep Learning Regression Methods

The accuracy of long-term wind power forecasting (WPF) is crucial for the efficient operation of grid systems. However, wind power generation is highly stochastic and intermittent due to the influence of weather, which makes long-term WPF less effective. Numerical weather prediction (NWP) data contains valuable weather forecast information, which can mitigate the negative effects of stochastic weather fluctuations on WPF. However, the accuracy of NWP data decreases over time, and multiple NWP data can have redundancy and errors that make it challenging to extract valid information. Reducing the variety and errors in NWP data and using more effective information extraction methods are essential for improving long-term WPF performance. In this article, we propose a novel long-term WPF hybrid model that corrects NWP wind speed and uses multi-scale deep learning regression prediction to exclude excessive NWP data. We use only the corrected NWP wind speed data to establish a nonlinear mapping relationship with actual power data. The validation case study shows that our proposed model reduces the mean squared error (MSE) and mean absolute error (MAE) by 65.0% and 43.8%, respectively, compared to the current state-of-the-art time series forecasting model in a seven-day forecasting scenario.

Optimization study of tourism total revenue prediction model based on the Grey Markov chain: a case study of Macau

<abstract> <p>The GM (1, 1) model, grounded in gray system theory, utilizes first-order cumulative data for forecasting. While offering simplicity and efficiency, its applicability is confined to such data. In light of the constraints inherent in the conventional gray GM (1, 1) prediction model when confronted with stochastic data fluctuations, the residual correction methodology was deployed to enhance the predictive efficacy of the GM (1, 1) model. Subsequently, an augmented model underwent refinement through the application of the Markov chain, giving rise to a sophisticated and optimized gray Markov chain prediction model. The efficacy of this novel model was substantiated through a case study involving the prediction of Macao's aggregate tourism revenue. A comparative analysis was conducted between the outcomes generated by the traditional gray prediction model, those of the refined prediction model, and the empirical data pertaining to tourism. This scrutiny validated the proficiency and precision of the optimized prediction model. The process of model optimization manifested a discernible enhancement in both predictive accuracy and stability, thereby broadening the prospective applications of gray prediction models. This endeavor aspired to furnish a scientifically grounded point of reference for the advancement of tourism within the Guangdong-Hong Kong-Macao Greater Bay Area and, indeed, throughout China. Moreover, it introduced a fresh methodology that held promise as a decision-making support mechanism for the developmental trajectory of Macao's tourism industry.</p> </abstract>

On the testability of the Károlyházy model

Károlyházy’s original proposal, suggesting that space-time fluctuations could be a source of decoherence in space, faced a significant challenge due to an unexpectedly high emission of radiation (13 orders of magnitude more than what was observed in the latest experiment). To address this issue, we reevaluated Károlyházy’s assumption that the stochastic metric fluctuation must adhere to a wave equation. By considering more general correlation functions of space-time fluctuations, we resolve the problem and consequently revive the aforementioned proposal.

A Threshold-Independent Approach to Stochastic Fluctuations in Optoelectronic Oscillators

A Threshold-Independent Approach to Stochastic Fluctuations in Optoelectronic Oscillators

Eternal inflation and collapse theories

The eternal inflation problem continues to be considered one of standard's cosmology most serious shortcomings. This arises when one considers the effects of “quantum fluctuations” on the zero mode of inflaton field during a Hubble time in the inflationary epoch.In the slow-roll regime it is quite clear that such quantum fluctuations could dwarf the classical rolling down of the inflaton, and with overwhelming probability this prevents inflation from ever ending. When one recognizes that quantum fluctuations can not be taken as synonymous of stochastic fluctuations, but rather intrinsic levels of indefiniteness in the quantities in question, one concludes that the eternal inflation problem simply does not exist. However, the same argument would serve to invalidate the account for the generation of the primordial seeds of cosmic structure as has been amply discussed elsewhere [1,2,3]. In order to do address that issue, one must explain the breaking of homogeneity and isotropy of the situation prevailing during the early inflationary epoch (at both the quantum and classical levels of the description). For that one needs to rely on some additional element, beyond those present in the traditional treatments. The so called spontaneous collapse theories offer a viable candidate for that element, namely the stochastic and spontaneous state reduction characteristic of those proposals possesses the basic features to break those symmetries. In fact, a version of the CSL theory adapted to the cosmological context has been shown to offer a satisfactory account for the origin the seeds of cosmic structure with an adequate power spectrum [2], and will serve as the basis of our analysis. However, once such stochastic collapse is introduced into the theoretical framework the eternal inflation problem has the potential reappear.In this manuscript we explore those issues in detail and discuss an avenue that seems to allow for a satisfactory account for the generation of the primordial inhomogeneities and anisotropies while freeing the theory from the eternal inflation problem.

Phase field crystal models with applications to laser deposition: A review.

In this article, we address the application of phase field crystal (PFC) theory, a hybrid atomistic-continuum approach, for modeling nanostructure kinetics encountered in laser deposition. We first provide an overview of the PFC methodology, highlighting recent advances to incorporate phononic and heat transport mechanisms. To simulate laser heating, energy is deposited onto a number of polycrystalline, two-dimensional samples through the application of initial stochastic fluctuations. We first demonstrate the ability of the model to simulate plasticity and recrystallization events that follow laser heating in the isothermal limit. Importantly, we also show that sufficient kinetic energy can cause voiding, which serves to suppress shock propagation. We subsequently employ a newly developed thermo-density PFC theory, coined thermal field crystal (TFC), to investigate laser heating of polycrystalline samples under non-isothermal conditions. We observe that the latent heat of transition associated with ordering can lead to long lasting metastable structures and defects, with a healing rate linked to the thermal diffusion. Finally, we illustrate that the lattice temperature simulated by the TFC model is in qualitative agreement with predictions of conventional electron-phonon two-temperature models. We expect that our new TFC formalism can be useful for predicting transient structures that result from rapid laser heating and re-solidification processes.